Question

Points A and B are at `(5 ,8 )` and `(7 ,3 )`, respectively. Point A is rotated counterclockwise about the origin by `pi` and dilated about point C by a factor of `5`. If point A is now at point B, what are the coordinates of point C?

Answer 1

`C=(-8,-43/4)`

Explanation:

`"under a counterclockwise rotation about the origin of "pi`

`• " a point "(x,y)to(-x,-y)`

`A(5,8)toA'(-5,-8)" where A' is the image of A"`

`vec(CB)=color(red)(5)vec(CA')`

`ulb-ulc=5(ula'-ulc)`

`ulb-ulc=5ula'-5ulc`

`4ulc=5ula'-ulb`

`color(white)(4ulc)=5((-5),(-8))-((7),(3))`

`color(white)(4ulc)=((-25),(-40))-((7),(3))=((-32),(-43))`

`ulc=1/4((-32),(-43))=((-8),(-43/4))`

`rArrC=(-8,-43/4)`